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Qiao W, Wang T, Yi H, Li X, Lv Y, Xi C, Wu R, Wang Y, Yu Y, Xing Y, Zhao J. Impact of a deep progressive reconstruction algorithm on low-dose or fast-scan PET image quality and Deauville score in patients with lymphoma. EJNMMI Phys 2025; 12:33. [PMID: 40169444 PMCID: PMC11961783 DOI: 10.1186/s40658-025-00739-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2024] [Accepted: 02/28/2025] [Indexed: 04/03/2025] Open
Abstract
BACKGROUND A deep progressive learning method for PET image reconstruction named deep progressive reconstruction (DPR) method was developed and presented in previous works. It has been shown in previous study that the DPR with one-third duration can maintain the image quality as OSEM with standard dose (3.7 MBq/kg). Subsequent studies have shown we can reduce the administered activity of 18F-FDG by up to 2/3 in a real-world deployment with DPR. The aim of this study is to assess the impact of the use of DPR on Deauville score (DS) and clinical interpretation of PET/CT in patients with lymphoma. METHODS A total of 87 lymphoma patients (age, 45.1 ± 14.9 years) who underwent 18F-FDG PET imaging for during or post-treatment follow-up from November 2020 to February 2024 were prospectively enrolled. The patients were randomly assigned to two groups, including the 1/3 standard dose group and the standard dose group. Forty-four patients were injected with 1/3 standard dose (1.23 MBq/kg) and scanned for 6 min per bed and were reconstructed: ordered-subsets expectation maximization (OSEM) with 6 min per bed (OSEM_6 min_1/3), OSEM_2 min_1/3 and DPR_2 min_1/3. Forty-three patients were scanned according to the standard protocol (3.7 MBq/kg) and were reconstructed: OSEM with 2 min per bed (OSEM_2 min_full), OSEM_40 s_full and DPR_40 s_full. Additionally, the conventional 5-point scale measurement analysis was performed and DS for lymphoma were determined in different groups. Wilcoxon signed-rank test was used to compare the mean values of liver SUVmax and mediastinal blood pool (MBP) SUVmax in each group. Likert scale and DS were evaluated using Wilcoxon signed rank test. RESULTS The patients with OSEM_6 min_1/3 and DPR_2 min_1/3 showed good image quality with 5(5,5) and 5(4,5) of Likert scoring, as well as the patients with OSEM_2 min_full and DPR_40 s_full. No significant difference was found between the OSEM_6 min_1/3 and DPR_2 min_1/3 groups in terms of liver SUVmax and MBP SUVmax (P = 0.452 and 0.430), as well as the patients with OSEM_2 min_full and DPR_40 s_full (P = 0.105 and 0.638). No significant difference was found between the OSEM_6 min_1/3 and DPR_2 min_1/3 groups in terms of lesion SUVmax (P = 0.080). There was a significant differences in lesion SUVmax between OSEM-2 min_full with DPR-40 s_full (P = 0.027). The DS results were consistent (100%) between OSEM-6 min_1/3 with DPR_2 min_1/3, and between OSEM-2 min_full with DPR-40 s_full, respectively. CONCLUSIONS DPR reconstruction demonstrated feasibility in reducing PET injection dose or scanning time, while ensuring the preservation of image quality and DS for during or post-treatment follow-up patients with lymphoma.
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Affiliation(s)
- Wenli Qiao
- Department of Nuclear Medicine, Shanghai General Hospital, Shanghai Jiaotong University School of Medicine, Shanghai, China
| | - Taisong Wang
- Department of Nuclear Medicine, Shanghai General Hospital, Shanghai Jiaotong University School of Medicine, Shanghai, China
| | - Hongyuan Yi
- United Imaging Healthcare Group Co., Ltd, Shanghai, China
| | - Xuebing Li
- Jincheng People's Hospital, Shanxi, China
| | - Yang Lv
- United Imaging Healthcare Group Co., Ltd, Shanghai, China
| | - Chen Xi
- United Imaging Healthcare Group Co., Ltd, Shanghai, China
| | - Runze Wu
- United Imaging Healthcare Group Co., Ltd, Shanghai, China
| | - Ying Wang
- United Imaging Healthcare Group Co., Ltd, Shanghai, China
| | - Ye Yu
- Hospital Affairs Office, Shanghai General Hospital, Shanghai Jiaotong University School of Medicine, Shanghai, China.
| | - Yan Xing
- Department of Nuclear Medicine, Shanghai General Hospital, Shanghai Jiaotong University School of Medicine, Shanghai, China.
| | - Jinhua Zhao
- Department of Nuclear Medicine, Shanghai General Hospital, Shanghai Jiaotong University School of Medicine, Shanghai, China.
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Hashimoto F, Onishi Y, Ote K, Tashima H, Reader AJ, Yamaya T. Deep learning-based PET image denoising and reconstruction: a review. Radiol Phys Technol 2024; 17:24-46. [PMID: 38319563 PMCID: PMC10902118 DOI: 10.1007/s12194-024-00780-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2023] [Revised: 01/03/2024] [Accepted: 01/04/2024] [Indexed: 02/07/2024]
Abstract
This review focuses on positron emission tomography (PET) imaging algorithms and traces the evolution of PET image reconstruction methods. First, we provide an overview of conventional PET image reconstruction methods from filtered backprojection through to recent iterative PET image reconstruction algorithms, and then review deep learning methods for PET data up to the latest innovations within three main categories. The first category involves post-processing methods for PET image denoising. The second category comprises direct image reconstruction methods that learn mappings from sinograms to the reconstructed images in an end-to-end manner. The third category comprises iterative reconstruction methods that combine conventional iterative image reconstruction with neural-network enhancement. We discuss future perspectives on PET imaging and deep learning technology.
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Affiliation(s)
- Fumio Hashimoto
- Central Research Laboratory, Hamamatsu Photonics K. K, 5000 Hirakuchi, Hamana-Ku, Hamamatsu, 434-8601, Japan.
- Graduate School of Science and Engineering, Chiba University, 1-33, Yayoicho, Inage-Ku, Chiba, 263-8522, Japan.
- National Institutes for Quantum Science and Technology, 4-9-1, Anagawa, Inage-Ku, Chiba, 263-8555, Japan.
| | - Yuya Onishi
- Central Research Laboratory, Hamamatsu Photonics K. K, 5000 Hirakuchi, Hamana-Ku, Hamamatsu, 434-8601, Japan
| | - Kibo Ote
- Central Research Laboratory, Hamamatsu Photonics K. K, 5000 Hirakuchi, Hamana-Ku, Hamamatsu, 434-8601, Japan
| | - Hideaki Tashima
- National Institutes for Quantum Science and Technology, 4-9-1, Anagawa, Inage-Ku, Chiba, 263-8555, Japan
| | - Andrew J Reader
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, SE1 7EH, UK
| | - Taiga Yamaya
- Graduate School of Science and Engineering, Chiba University, 1-33, Yayoicho, Inage-Ku, Chiba, 263-8522, Japan
- National Institutes for Quantum Science and Technology, 4-9-1, Anagawa, Inage-Ku, Chiba, 263-8555, Japan
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Zhu W, Lee SJ. Similarity-Driven Fine-Tuning Methods for Regularization Parameter Optimization in PET Image Reconstruction. SENSORS (BASEL, SWITZERLAND) 2023; 23:5783. [PMID: 37447633 DOI: 10.3390/s23135783] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Revised: 06/18/2023] [Accepted: 06/19/2023] [Indexed: 07/15/2023]
Abstract
We present an adaptive method for fine-tuning hyperparameters in edge-preserving regularization for PET image reconstruction. For edge-preserving regularization, in addition to the smoothing parameter that balances data fidelity and regularization, one or more control parameters are typically incorporated to adjust the sensitivity of edge preservation by modifying the shape of the penalty function. Although there have been efforts to develop automated methods for tuning the hyperparameters in regularized PET reconstruction, the majority of these methods primarily focus on the smoothing parameter. However, it is challenging to obtain high-quality images without appropriately selecting the control parameters that adjust the edge preservation sensitivity. In this work, we propose a method to precisely tune the hyperparameters, which are initially set with a fixed value for the entire image, either manually or using an automated approach. Our core strategy involves adaptively adjusting the control parameter at each pixel, taking into account the degree of patch similarities calculated from the previous iteration within the pixel's neighborhood that is being updated. This approach allows our new method to integrate with a wide range of existing parameter-tuning techniques for edge-preserving regularization. Experimental results demonstrate that our proposed method effectively enhances the overall reconstruction accuracy across multiple image quality metrics, including peak signal-to-noise ratio, structural similarity, visual information fidelity, mean absolute error, root-mean-square error, and mean percentage error.
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Affiliation(s)
- Wen Zhu
- Department of Electrical and Electronic Engineering, Pai Chai University, Daejeon 35345, Republic of Korea
| | - Soo-Jin Lee
- Department of Electrical and Electronic Engineering, Pai Chai University, Daejeon 35345, Republic of Korea
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Li S, Gong K, Badawi RD, Kim EJ, Qi J, Wang G. Neural KEM: A Kernel Method With Deep Coefficient Prior for PET Image Reconstruction. IEEE TRANSACTIONS ON MEDICAL IMAGING 2023; 42:785-796. [PMID: 36288234 PMCID: PMC10081957 DOI: 10.1109/tmi.2022.3217543] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Image reconstruction of low-count positron emission tomography (PET) data is challenging. Kernel methods address the challenge by incorporating image prior information in the forward model of iterative PET image reconstruction. The kernelized expectation-maximization (KEM) algorithm has been developed and demonstrated to be effective and easy to implement. A common approach for a further improvement of the kernel method would be adding an explicit regularization, which however leads to a complex optimization problem. In this paper, we propose an implicit regularization for the kernel method by using a deep coefficient prior, which represents the kernel coefficient image in the PET forward model using a convolutional neural-network. To solve the maximum-likelihood neural network-based reconstruction problem, we apply the principle of optimization transfer to derive a neural KEM algorithm. Each iteration of the algorithm consists of two separate steps: a KEM step for image update from the projection data and a deep-learning step in the image domain for updating the kernel coefficient image using the neural network. This optimization algorithm is guaranteed to monotonically increase the data likelihood. The results from computer simulations and real patient data have demonstrated that the neural KEM can outperform existing KEM and deep image prior methods.
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Juengling FD, Wuest F, Kalra S, Agosta F, Schirrmacher R, Thiel A, Thaiss W, Müller HP, Kassubek J. Simultaneous PET/MRI: The future gold standard for characterizing motor neuron disease-A clinico-radiological and neuroscientific perspective. Front Neurol 2022; 13:890425. [PMID: 36061999 PMCID: PMC9428135 DOI: 10.3389/fneur.2022.890425] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/05/2022] [Accepted: 07/20/2022] [Indexed: 01/18/2023] Open
Abstract
Neuroimaging assessment of motor neuron disease has turned into a cornerstone of its clinical workup. Amyotrophic lateral sclerosis (ALS), as a paradigmatic motor neuron disease, has been extensively studied by advanced neuroimaging methods, including molecular imaging by MRI and PET, furthering finer and more specific details of the cascade of ALS neurodegeneration and symptoms, facilitated by multicentric studies implementing novel methodologies. With an increase in multimodal neuroimaging data on ALS and an exponential improvement in neuroimaging technology, the need for harmonization of protocols and integration of their respective findings into a consistent model becomes mandatory. Integration of multimodal data into a model of a continuing cascade of functional loss also calls for the best attempt to correlate the different molecular imaging measurements as performed at the shortest inter-modality time intervals possible. As outlined in this perspective article, simultaneous PET/MRI, nowadays available at many neuroimaging research sites, offers the perspective of a one-stop shop for reproducible imaging biomarkers on neuronal damage and has the potential to become the new gold standard for characterizing motor neuron disease from the clinico-radiological and neuroscientific perspectives.
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Affiliation(s)
- Freimut D. Juengling
- Division of Oncologic Imaging, University of Alberta, Edmonton, AB, Canada
- Neuroscience and Mental Health Institute, University of Alberta, Edmonton, AB, Canada
- Faculty of Medicine, University Bern, Bern, Switzerland
| | - Frank Wuest
- Division of Oncologic Imaging, University of Alberta, Edmonton, AB, Canada
| | - Sanjay Kalra
- Neuroscience and Mental Health Institute, University of Alberta, Edmonton, AB, Canada
- Department of Neurology, University of Alberta, Edmonton, AB, Canada
| | - Federica Agosta
- Division of Neuroscience, San Raffaele Scientific Institute, University Vita Salute San Raffaele, Milan, Italy
| | - Ralf Schirrmacher
- Division of Oncologic Imaging, University of Alberta, Edmonton, AB, Canada
- Medical Isotope and Cyclotron Facility, University of Alberta, Edmonton, AB, Canada
| | - Alexander Thiel
- Lady Davis Institute for Medical Research, Department of Neurology and Neurosurgery, McGill University, Montreal, QC, Canada
| | - Wolfgang Thaiss
- Department of Nuclear Medicine, University of Ulm Medical Center, Ulm, Germany
- Department of Diagnostic and Interventional Radiology, University of Ulm Medical Center, Ulm, Germany
| | - Hans-Peter Müller
- Department of Neurology, Ulm University Medical Center, Ulm, Germany
| | - Jan Kassubek
- Department of Neurology, Ulm University Medical Center, Ulm, Germany
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Li X, Li Y, Chen P, Li F. Combining convolutional sparse coding with total variation for sparse-view CT reconstruction. APPLIED OPTICS 2022; 61:C116-C124. [PMID: 35201005 DOI: 10.1364/ao.445315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/11/2021] [Accepted: 01/13/2022] [Indexed: 06/14/2023]
Abstract
Conventional dictionary-learning-based computed tomography (CT) reconstruction methods extract patches from an original image to train, ignoring the consistency of pixels in overlapping patches. To address the problem, this paper proposes a method combining convolutional sparse coding (CSC) with total variation (TV) for sparse-view CT reconstruction. The proposed method inherits the advantages of CSC by directly processing the whole image without dividing it into overlapping patches, which preserves more details and reduces artifacts caused by patch aggregation. By introducing a TV regularization term to enhance the constraint of the image domain, the noise can be effectively further suppressed. The alternating direction method of multipliers algorithm is employed to solve the objective function. Numerous experiments are conducted to validate the performance of the proposed method in different views. Qualitative and quantitative results show the superiority of the proposed method in terms of noise suppression, artifact reduction, and image details recovery.
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Miller RJH, Singh A, Dey D, Slomka P. Artificial Intelligence and Cardiac PET/Computed Tomography Imaging. PET Clin 2021; 17:85-94. [PMID: 34809873 DOI: 10.1016/j.cpet.2021.06.011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Artificial intelligence is an important technology, with rapidly expanding applications for cardiac PET. We review the common terminology, including methods for training and testing, which are fundamental to understanding artificial intelligence. Next, we highlight applications to improve image acquisition, reconstruction, and segmentation. Computed tomographic imaging is commonly acquired in conjunction with PET and various artificial intelligence methods have been applied, including methods to automatically extract anatomic information or generate synthetic attenuation images. Last, we describe methods to automate disease diagnosis or risk stratification. This summary highlights the current and future clinical applications of artificial intelligence to cardiovascular PET imaging.
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Affiliation(s)
- Robert J H Miller
- Department of Cardiac Sciences, University of Calgary, GAA08 HRIC, 3230 Hospital Drive NW, Calgary AB, T2N 4Z6, Canada
| | - Ananya Singh
- Departments of Imaging and Medicine, Cedars-Sinai Medical Center, 8700 Beverly Blvd, Suite Metro 203, Los Angeles, CA 90048, USA
| | - Damini Dey
- Departments of Imaging and Medicine, Cedars-Sinai Medical Center, 8700 Beverly Blvd, Suite Metro 203, Los Angeles, CA 90048, USA
| | - Piotr Slomka
- Departments of Imaging and Medicine, Cedars-Sinai Medical Center, 8700 Beverly Blvd, Suite Metro 203, Los Angeles, CA 90048, USA.
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Gong K, Kim K, Cui J, Wu D, Li Q. The Evolution of Image Reconstruction in PET: From Filtered Back-Projection to Artificial Intelligence. PET Clin 2021; 16:533-542. [PMID: 34537129 DOI: 10.1016/j.cpet.2021.06.004] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
PET can provide functional images revealing physiologic processes in vivo. Although PET has many applications, there are still some limitations that compromise its precision: the absorption of photons in the body causes signal attenuation; the dead-time limit of system components leads to the loss of the count rate; the scattered and random events received by the detector introduce additional noise; the characteristics of the detector limit the spatial resolution; and the low signal-to-noise ratio caused by the scan-time limit (eg, dynamic scans) and dose concern. The early PET reconstruction methods are analytical approaches based on an idealized mathematical model.
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Affiliation(s)
- Kuang Gong
- Department of Radiology, Center for Advanced Medical Computing and Analysis, Gordon Center for Medical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, MA, USA
| | - Kyungsang Kim
- Department of Radiology, Center for Advanced Medical Computing and Analysis, Gordon Center for Medical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, MA, USA
| | - Jianan Cui
- Department of Radiology, Center for Advanced Medical Computing and Analysis, Gordon Center for Medical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, MA, USA
| | - Dufan Wu
- Department of Radiology, Center for Advanced Medical Computing and Analysis, Gordon Center for Medical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, MA, USA
| | - Quanzheng Li
- Department of Radiology, Center for Advanced Medical Computing and Analysis, Gordon Center for Medical Imaging, Massachusetts General Hospital, Harvard Medical School, Boston, MA, USA.
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Xie N, Gong K, Guo N, Qin Z, Wu Z, Liu H, Li Q. Rapid high-quality PET Patlak parametric image generation based on direct reconstruction and temporal nonlocal neural network. Neuroimage 2021; 240:118380. [PMID: 34252526 DOI: 10.1016/j.neuroimage.2021.118380] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2021] [Revised: 07/04/2021] [Accepted: 07/07/2021] [Indexed: 11/25/2022] Open
Abstract
Parametric imaging based on dynamic positron emission tomography (PET) has wide applications in neurology. Compared to indirect methods, direct reconstruction methods, which reconstruct parametric images directly from the raw PET data, have superior image quality due to better noise modeling and richer information extracted from the PET raw data. For low-dose scenarios, the advantages of direct methods are more obvious. However, the wide adoption of direct reconstruction is inevitably impeded by the excessive computational demand and deficiency of the accessible raw data. In addition, motion modeling inside dynamic PET image reconstruction raises more computational challenges for direct reconstruction methods. In this work, we focused on the 18F-FDG Patlak model, and proposed a data-driven approach which can estimate the motion corrected full-dose direct Patlak images from the dynamic PET reconstruction series, based on a proposed novel temporal non-local convolutional neural network. During network training, direct reconstruction with motion correction based on full-dose dynamic PET sinograms was performed to obtain the training labels. The reconstructed full-dose /low-dose dynamic PET images were supplied as the network input. In addition, a temporal non-local block based on the dynamic PET images was proposed to better recover the structural information and reduce the image noise. During testing, the proposed network can directly output high-quality Patlak parametric images from the full-dose /low-dose dynamic PET images in seconds. Experiments based on 15 full-dose and 15 low-dose 18F-FDG brain datasets were conducted and analyzed to validate the feasibility of the proposed framework. Results show that the proposed framework can generate better image quality than reference methods.
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Affiliation(s)
- Nuobei Xie
- College of Optical Science and Engineering, Zhejiang University, 38 Zheda Road, Building 3, Hangzhou 310027, China; Center for Advanced Medical Computing and Analysis, Massachusetts General Hospital and Harvard Medical School, 55 Fruit St, White 427, 125 Nashua Street, Suite 660, Boston, MA 02114, United States.
| | - Kuang Gong
- Center for Advanced Medical Computing and Analysis, Massachusetts General Hospital and Harvard Medical School, 55 Fruit St, White 427, 125 Nashua Street, Suite 660, Boston, MA 02114, United States.
| | - Ning Guo
- Center for Advanced Medical Computing and Analysis, Massachusetts General Hospital and Harvard Medical School, 55 Fruit St, White 427, 125 Nashua Street, Suite 660, Boston, MA 02114, United States
| | - Zhixing Qin
- Department of Nuclear Medicine, First Hospital of Shanxi Medical University, Taiyuan, Shanxi, China
| | - Zhifang Wu
- Department of Nuclear Medicine, First Hospital of Shanxi Medical University, Taiyuan, Shanxi, China
| | - Huafeng Liu
- College of Optical Science and Engineering, Zhejiang University, 38 Zheda Road, Building 3, Hangzhou 310027, China.
| | - Quanzheng Li
- Center for Advanced Medical Computing and Analysis, Massachusetts General Hospital and Harvard Medical School, 55 Fruit St, White 427, 125 Nashua Street, Suite 660, Boston, MA 02114, United States.
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Ping Z, Zhang T, Gong L, Zhang C, Zuo S. Miniature Flexible Instrument with Fibre Bragg Grating-Based Triaxial Force Sensing for Intraoperative Gastric Endomicroscopy. Ann Biomed Eng 2021; 49:2323-2336. [PMID: 33880633 DOI: 10.1007/s10439-021-02781-4] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2020] [Accepted: 04/11/2021] [Indexed: 11/28/2022]
Abstract
Optical biopsy methods, such as probe-based endomicroscopy, can be used to identify early-stage gastric cancer in vivo. However, it is difficult to scan a large area of the gastric mucosa for mosaicking during endoscopy. In this work, we propose a miniaturised flexible instrument based on contact-aided compliant mechanisms and fibre Bragg grating (FBG) sensing for intraoperative gastric endomicroscopy. The instrument has a compact design with an outer diameter of 2.7 mm, incorporating a central channel with a diameter of 1.9 mm for the endomicroscopic probe to pass through. Experimental results show that the instrument can achieve raster trajectory scanning over a large tissue surface with a positioning accuracy of 0.5 mm. The tip force sensor provides a 4.6 mN resolution for the axial force and 2.8 mN for transverse forces. Validation with random samples shows that the force sensor can provide consistent and accurate three-axis force detection. Endomicroscopic imaging experiments were conducted, and the flexible instrument performed no gap scanning (mosaicking area more than 3 mm2) and contact force monitoring during scanning, demonstrating the potential of the system in clinical applications.
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Affiliation(s)
- Zhongyuan Ping
- Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin, 300072, China
| | - Tianci Zhang
- Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin, 300072, China
| | - Lun Gong
- Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin, 300072, China
| | - Chi Zhang
- Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin, 300072, China
| | - Siyang Zuo
- Key Laboratory of Mechanism Theory and Equipment Design of Ministry of Education, Tianjin University, Tianjin, 300072, China.
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